Análisis de Incidentes de Actividad Criminal en Colombia (2023) Usando Modelos de Regresión para Datos de Conteo.

Abstract

This study presents a statistical analysis of thefts from businesses in Colombia, using data from the country’s 32 departments. The primary objective is to identify and model the economic, social, and spatial factors that explain the incidence of this type of crime, with the aim of providing analytical tools for the formulation of more effective public policies. The analysis begins with an initial exploration of the data, during which significant spatial patterns of thefts were identified, confirmed by a positive and statistically significant Moran’s Index. This finding suggests spatial dependence between departments. Based on this diagnostic, Poisson and Negative Binomial Regression Models were implemented, adjusted for population as an exposure variable, to model theft rates instead of absolute counts, thereby facilitating comparability across regions with different population sizes. The parsimonious Poisson Model proved to be a robust tool for analysis; however, the presence of overdispersion in the data justified the implementation of the Negative Binomial Model, which includes an additional parameter to capture excess variability. The results of both models identified key factors influencing the reduction of thefts from businesses: GDP, levels of monetary poverty, crime rates, and a spatial effect measured by the lag of thefts in neighboring departments. In particular, GDP showed a negative and statistically significant effect, underscoring the role of economic development in crime mitigation. The lagged thefts term highlighted the importance of spatial effects in the propagation or containment of thefts, indicating that shared departmental dynamics significantly influence the observed outcomes. The evaluation of residuals from both models, through graphs and Moran’s Index analysis, confirmed the absence of spatial autocorrelation in the residuals, validating the statistical and spatial specifications of the adjusted models. Moreover, the Negative Binomial Model demonstrated superior fit according to the AIC and the inclusion of over-dispersion (α = 0.1149). In conclusion, the study underscores the importance of economic and spatial factors in explaining thefts from businesses, highlighting the need for coordinated regional policies and approaches based on economic development to address this issue. The implementation of joint strategies between neighboring departments and the continuous use of advanced models to monitor and evaluate crime patterns are recommended. This work provides a robust and replicable analytical framework for the study of criminological phenomena in spatial contexts.